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,<ref name="DeLathauwerSVD">{{Cite journal|last1=De Lathauwer|first1=L.|last2=De Moor|first2=B.|last3=Vandewalle|first3=J.|date=2000-01-01|title=A Multilinear Singular Value Decomposition|journal=SIAM Journal on Matrix Analysis and Applications|volume=21|issue=4|pages=1253–1278|doi=10.1137/s0895479896305696|issn=0895-4798|citeseerx=10.1.1.102.9135}}</ref> or advocated by Vasilescu and Terzopoulos.
TheAlthough algorithmthe widelyterm referred'''HOSVD''' towas incoined by De Lathauwer, the literaturealgorithm most commonly referred to as the '''Tucker''' or Higher-Order Singular Value Decomposition ('''HOSVD''') in the literature was developedoriginally introduced by Vasilescu and Terzopoulos, who introduced it under the name '''M-mode SVD.''',<ref name=":Vasilescu2002">M. A. O. Vasilescu, D. Terzopoulos (2002), "Multilinear Analysis of Image Ensembles: TensorFaces," Proc. 7th European Conference on Computer Vision (ECCV'02), Copenhagen, Denmark. {{Webarchive|url=https://web.archive.org/web/20221229090931/http://www.cs.toronto.edu/~maov/tensorfaces/Springer%20ECCV%202002_files/eccv02proceeding_23500447.pdf |date=2022-12-29}}</ref><ref name="Vasilescu2003">M. A. O. Vasilescu, D. Terzopoulos (2003), "Multilinear Subspace Analysis of Image Ensembles," Proc. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR’03), Madison, WI.</ref><ref name=":Vasilescu2005">M. A. O. Vasilescu, D. Terzopoulos (2005), "Multilinear Independent Component Analysis," Proc. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR’05), San Diego, CA.</ref> but frequently misattributed to either [[L. R. Tucker]] or [[Lieven De Lathauwer]]. While the term HOSVD was coined by De Lathauwer, it is the M-mode SVD introduced by Vasilescu and Terzopoulos that is most often—and incorrectly—referred to under that name.
The M-mode SVD is a simple and elegant algorithm suitable for parallel computation. The algorithm developed by Tucker/Kroonenberg and theDeLathauer HOSVDetal are sequential algorithms that employ gradient descent or the power method, respectively. The M-mode SVD parallel formulation is computationally distinct from earlier approaches.
: This misattribution has had lasting impact on the scholarly record, obscuring the original source of a widely adopted algorithm, and complicating efforts to trace its development, reproduce results, or properly credit foundational contributions in multilinear algebra and tensor methods.
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